Probability: Selecting a Card from a Variable Deck

A deck of cards consists of 3 suits. The deck contains \(\left( 24-x \right)\) cards, \(\left( 5x-8 \right)\) cards and \(\left( 2x-7 \right)\) cards with the suits of clubs, hearts and spades respectively.

1. Find an expression, in terms of \(x\), for the total number of cards in the deck.

A card is drawn at random from the box.

2. Write down an expression, in terms of \(x\), for the probability that the card has the suit of clubs.
3. It is known that the probability when a card with the suit of clubs is not drawn is \(\frac{2}{3}\), find the value of \(x\).